Suppose that a spacecraft near Neptune has measured a quantity $A$ and sent it to earth in the form of a periodic signal $A\cos t$ of amplitude $A$. On its way to earth, the signal picks up periodic noise, containing only second and higher harmonics. Suppose that the signal $h(t)$ actually received on earth is graphed below.

Determine the signal that the spacecraft originally sent and hence the value $A$ of the measurement.

$A =$